Answer:
(f o h)(x) = -10x + 32
General Formulas and Concepts:
<u>Pre-Algebra</u>
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
f(x) = 2x³ + 8
h(x) = ∛(12 - 5x)
(f o h)(x) is f(h(x))
<u>Step 2: Find Composite Function</u>
- Substitute: (f o h)(x) = 2(∛(12 - 5x))³ + 8
- Evaluate: (f o h)(x) = 2(12 - 5x) + 8
- Distribute 2: (f o h)(x) = 24 - 10x + 8
- Combine like terms: (f o h)(x) = -10x + 32
And we have our final answer!
Answer:
(0,0)
Step-by-step explanation:
The coordinates of C now are (-7,-5).
Moving C -3 on the x-axis will move -7 - 3 = -10. C is now located on (-10,-5).
Moving C +5 on the y-axis will move -5 + 5 = 0. C is now located on (-10,0).
Moving C on the y-axis +10 will move -10 + 10 = 0. C is now located on (0,0).
C is translated to (0,0).
We need to FOIL that out and then get it into standard form to see what our A, B, and C are. FOILing gives us
. If we move the 7 over by subtraction and set it equal to 0, we have
. In order to avoid a negative leading coefficient, we can change all the signs to get
so A = 1, B = 0, C = -18, first choice above.
Let's use the variable "r" to represent the investment rate of the stocks:
2r(500) + r(800) = 45
1000r + 800r = 45
1800r = 45
r = 0.025
2r = 0.05
The $500 is invested at 5%
the volume for pretty much any shape/object is length times width times height
